CODIMENSION-2 HOPF BIFURCATION OF A TWO-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM

Codimension-2 Hopf bifurcation problem of a two-degree-of-freedom system vibrating against a rigid surface is investigated in this paper. The four-dimensional Poincaré map of the vibro-impact system is reduced to a two-dimensional normal form by virtue of a center manifold reduction and a normal form technique. Then the theory of Hopf bifurcation of maps in R2is applied to conclude the existence of codimension-2 Hopf bifurcation of the vibro-impact system. The quasi-periodic response of the system by theoretical analysis is well supported by numerical simulations. It is shown that there exists codimension-2 Hopf bifurcation in multi-degree-of-freedom vibro-impact systems. The codimension-2 tori doubling phenomenon and the routes of quasi-periodic impacts to chaos are reported briefly.